Question

tìm x:

\(\left(x-\frac{2}{3}\right)^2=\frac{5}{6}\)

Answer 1

\(\left(x-\frac{2}{3}\right)^2=\frac{5}{6}\\ \left(x-\frac{2}{3}\right)^2=\left(\frac{\sqrt{30}}{6}\right)^2=\left(\frac{-\sqrt{30}}{6}\right)^2\\ \Rightarrow\left[{}\begin{matrix}x-\frac{2}{3}=\frac{\sqrt{30}}{6}\\x-\frac{2}{3}=\frac{-\sqrt{30}}{6}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\frac{\sqrt{30}}{6}+\frac{2}{3}\\x=\frac{-\sqrt{30}}{6}+\frac{2}{3}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\frac{4+\sqrt{30}}{6}\\x=\frac{4-\sqrt{30}}{6}\end{matrix}\right.\)

Vậy \(x\in\left\{\frac{4+\sqrt{30}}{6};\frac{4-\sqrt{30}}{6}\right\}\)